新西兰 - New Zealand

大多数带“国”的称呼都是双音节的词（包含“国”字）。

Most of the names with 'country' are two-syllable words (including the word 'country' which pronounced 'guo' in Chinese ).

For example 

England - 英国（ying guo），America - 美国(mei guo)，Germany - 德国（de guo）, Korea - 韩国（han guo），Tailand - 泰国（tai guo）, etc.

三音节及以上的国名一般不加“国”。

Country names of three syllables and above generally do not include 'country' in Chinese.

For example

New Zealand - 新西兰（xin xi lan），Austria - 澳大利亚（ao da li ya）， Canada-加拿大（jia na da），Japan - 日本（ri ben）

加上“人”的规则也一样。 It's the same rule to describe people where they come from, and just put the '人（ren）' behind it.

For example

American - （美国）人； New Zealander - （新西兰）人

BTW, You can consider that as it's for the convenience of pronunciation and expression.

新西兰 - New Zealand

The general rule is that when in the old days, the name of the country is translated by "meaning"  国 is added.  For example, 英国 (country of heroes), 美国 (country of the beautiful, from the song "America the beautiful" and emphasis for the sound "mei"), 德国 (country of virtue), 法国 (country of law, from Napoleanic code).  When a country's name is transliterated, then 国 is dropped.  For example, 英格蘭 (England), 意大利 (Italy) and of course, "New Zealand" and other names for recent countries became known to China. Sino-influenced countries like Japan, Vietnam and Korea, the names are used according to the Chinese characters used by the natives.

It is easier and more convenient to transliterate than to translate by meaning.

新西兰 - New Zealand

加不加都是可以的，因为新西兰是个国家，如果加了，除非对方不知道，都可以的~

新西兰 - New Zealand

都是正确的

新西兰 - New Zealand

People in different countries have different names. It's not the same thing.

Australian = 澳大利亚人 没有国

American = 美国人  有国

Chinese = 中国人     有国